Related papers: Inequalities on Six Points in a $\mathrm{CAT}(0)$ …
In this paper known results of symmetric orthogonality, as introduced by G. Birkhoff, and non-expansive nearest point projections are extended from the linear to the metric setting. If the space has non-positive curvature in the sense…
There are various non-equivalent definitions of locality. Three of them, impossibility of instantaneous communication, impossibility of action-at-a-distance, and impossibility of faster-than-light travel, while not fully implying each…
Cianci and Ottina proved that a homotopically trivial non-contractible finite $T_0$-space cannot have fewer than nine points and classified all such spaces with exactly nine points. The present paper completes the classification for spaces…
We obtain a necessary and sufficient condition for the existence of equivariant real structures on complex symmetric spaces for semisimple groups and discuss how to determine the number of equivalence classes for such structures.
We introduce a new family of shift spaces --- the subordinate shifts. Using subordinate shifts we prove in an elementary way that for every nonnegative real number $t$ there is a shift space with entropy $t$.
This paper is inspired by the paper of Leonetti, Russo and Somaglia [\textit{Dense lineability and spaceability in certain subsets of $\ell_\infty$.} Bull. London Math. Soc., 55: 2283--2303 (2023)] and the lineability problems raised…
We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube…
In the paper we study properties of the set of critical points for self-similar sets. We introduce simple condition that implies at most countably many critical values and we construct a self-similar set with uncountable set of critical…
The matrix version of the entropy-power inequality for real or complex coefficients and variables is proved using a transportation argument that easily settles the equality case. An application to blind source extraction is given.
As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well-defined since quasi-isometric CAT(0) spaces can have non-homeomorphic boundaries. We introduce a new type of boundary for a CAT(0) space, called the…
The analogue of Hilbert's tenth problem over $\mathbb{Q}$ asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as one of the main open problems in the area of undecidability…
In this paper, we establish some common fixed point results for two pairs of weakly compatible mappings in the setting of $C$-complex valued metric space. Also, as application of the proved result, we obtain the existence and uniqueness of…
We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities (for submanifolds) to hold.
After a short introduction to the general notion of Borel fields of metric spaces we introduce the notion of the action of an equivalence relation on such fields. Then, we specify the study to the Borel fields of proper CAT(0) spaces and we…
In this paper, we prove several fixed point theorems on both of normal partially ordered Banach spaces and regular partially ordered Banach spaces by using the normality, regularity, full regularity, and chain -complete property. Then, by…
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…
We prove a half-space Bernstein theorem for Allen-Cahn equation. More precisely, we show that every solution $u$ of the Allen-Cahn equation in the half-space $\overline{\mathbb{R}^n_+}:=\{(x_1,x_2,\cdots,x_n)\in\mathbb{R}^n:\,x_1\geq 0\}$…
Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their…
It is argued that the concept of ``physical quantities possessed by the system'' is both redundant and inappropriate. We have examined two versions of the concept of ``possessed values'': one identical with the observed values and the other…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.